Calculus of Variations and Geometric Measure Theory

A. Carbotti - S. Cito - D. A. La Manna - D. Pallara

Gamma-convergence of fractional Gaussian perimeter

created by carbotti on 30 Mar 2021
modified on 08 Dec 2021


Published Paper

Inserted: 30 mar 2021
Last Updated: 8 dec 2021

Journal: Advances in Calculus of Variations
Pages: 30
Year: 2021

ArXiv: 2103.16598 PDF

30 pages, 3 figures


We prove the $\Gamma$-convergence of the renormalised fractional Gaussian $s$-perimeter to the Gaussian perimeter as $s\to 1^-$. Our definition of fractional perimeter comes from that of the fractional powers of Ornstein-Uhlenbeck operator given via Bochner subordination formula. As a typical feature of the Gaussian setting, the constant appearing in front of the $\Gamma$-limit does not depend on the dimension.

Keywords: Gamma-convergence, Fractional perimeters, Gaussian analysis